Achieving matrix consistency in AHP through linearization

Matrices used in the analytic hierarchy process (AHP) compile expert knowledge as pairwise comparisons among various criteria and alternatives in decision-making problems. Many items are usually considered in the same comparison process and so judgment is not completely consistent – and sometimes th...

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Bibliographic Details
Published in:Applied mathematical modelling 2011-09, Vol.35 (9), p.4449-4457
Main Authors: Benítez, Julio, Delgado-Galván, Xitlali, Izquierdo, Joaquín, Pérez-García, Rafael
Format: Article
Language:English
Subjects:
Analytic hierarchy process
Applied sciences
Consistency
Decision making
Decision theory. Utility theory
Earth sciences
Earth, ocean, space
Exact sciences and technology
Exact solutions
Hydrology. Hydrogeology
Leakage management
Linearization
Mathematical analysis
Mathematical models
Operational research and scientific management
Operational research. Management science
Policies
Water resources
Water supplies
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Summary:Matrices used in the analytic hierarchy process (AHP) compile expert knowledge as pairwise comparisons among various criteria and alternatives in decision-making problems. Many items are usually considered in the same comparison process and so judgment is not completely consistent – and sometimes the level of consistency may be unacceptable. Different methods have been used in the literature to achieve consistency for an inconsistent matrix. In this paper we use a linearization technique that provides the closest consistent matrix to a given inconsistent matrix using orthogonal projection in a linear space. As a result, consistency can be achieved in a closed form. This is simpler and cheaper than for methods relying on optimisation, which are iterative by nature. We apply the process to a real-world decision-making problem in an important industrial context, namely, management of water supply systems regarding leakage policies – an aspect of water management to which great sums of money are devoted every year worldwide.
ISSN:0307-904X
DOI:10.1016/j.apm.2011.03.013